Chem Differential Eq HW Solutions Fall 2011 151

Chem Differential Eq HW Solutions Fall 2011 151 - x ( t ) =...

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Section 12.1 Green’s Theorem and Identities 151 9. Take u ( x, y )= y and v ( x, y )= x . Then 2 v =0 , u =(0 , 1), v =(1 , 0), so u ·∇ v = 0 and, by (9), ± C y ∂x ∂n ds = ± C u ∂v ∂n ds = ± Γ 0 ds =0 . 13. Same solution as in Example 1. Use Theorem 2 instead of Theorem 1. 17.
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Unformatted text preview: x ( t ) = a cos t , y ( t ) = b sin t , dy = b cos tdt , 0 t 2 . Area = C xdy = 2 a cos tb sin tdt = ab 2 cos 2 tdt = ab 2 1 + cos(2 t ) 2 dt = ab....
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.

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